The side of a cube is increasing at a rate of 4 cm/sec. Find the rate of change of the volume of the cube when its side is 5 cm.

Options

A. 350 `cm^(3)`/sec
B. 450 `cm^(3)`/sec
C. 200 `cm^(3)`/sec
D. 300 `cm^(3)`/sec

Answer

D

Explanation

Let x =side of the cube and V = volume of the cube.
`:. V = x^(3)`
Give that x = 5 cm and `(dx)/(dt)` = 4cm/sec.
Now `(dV)/(dt)=3x^(2).(dx)/(dt)`
At x = 5 cm,
`(dV)/(dt)=3(5)^(2).4 cm^(3)`/sec
=300 `cm^(3)`/sec
Therefore the volume will be increased at 300 `cm^(3)`/sec.